Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-2x-y &= -4 \\ -x+2y &= 8\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $2$ and the bottom equation by $1$ $\begin{align*}-4x-2y &= -8\\ -x+2y &= 8\end{align*}$ Add the top and bottom equations. $-5x = 0$ Divide both sides by $-5$ and reduce as necessary. $x = 0$ Substitute $0$ for $x$ in the top equation. $-2( 0)-y = -4$ $-y = -4$ $-y = -4$ $y = 4$ The solution is $\enspace x = 0, \enspace y = 4$.